The Equilibrium Constant Kc

What is Kc and what does it represent?

Kc is the equilibrium constant expressed in terms of concentrations. It is a numerical value that quantifies the position of equilibrium for a reversible reaction at a given temperature. It is calculated using the equilibrium concentrations of all species in the reaction, with concentrations measured in mol dm⁻³. Kc only changes with temperature — it is unaffected by changes in concentration, pressure, or the addition of a catalyst.

How do you write the Kc expression for a homogeneous equilibrium?

For a general homogeneous equilibrium aA + bB ⇌ cC + dD, the Kc expression is:

Kc = [C]ᶜ[D]ᵈ / [A]ᵃ[B]ᵇ

Where square brackets [ ] denote equilibrium concentrations in mol dm⁻³, and the powers are the stoichiometric coefficients from the balanced equation. The concentrations used must be equilibrium concentrations, not initial concentrations.

Write the Kc expression for the following reactions:

N₂(g) + 3H₂(g) ⇌ 2NH₃(g)

H₂(g) + I₂(g) ⇌ 2HI(g)

• Kc = [HI]² / ([H₂][I₂])

• Kc = [CH₃COOC₂H₅][H₂O] / ([CH₃COOH][C₂H₅OH])

What are the units of Kc, and how do you work them out?

The units of Kc depend on the overall change in the number of moles between products and reactants (Δn). Substitute mol dm⁻³ for each concentration term and simplify. Note: the OCR specification at AS level states that you do not need to determine the units of Kc — you may simply be required to calculate the numerical value. However, it is good practice to know that units vary and may be mol dm⁻³, mol² dm⁻⁶, dm³ mol⁻¹ etc. depending on the reaction, or dimensionless (no units) when Δn = 0.

How do you calculate Kc from given equilibrium concentrations?

Write the Kc expression for the equation, substitute the equilibrium concentrations into the expression, and calculate. Always use equilibrium concentrations — if you are given initial concentrations and moles reacted, calculate equilibrium concentrations first by: equilibrium concentration = (initial moles ± moles reacted) ÷ volume of mixture (in dm³).

Worked example: at equilibrium, [H₂] = 0.10 mol dm⁻³, [I₂] = 0.10 mol dm⁻³, [HI] = 0.80 mol dm⁻³. Calculate Kc for H₂(g) + I₂(g) ⇌ 2HI(g).

Kc = [HI]² / ([H₂][I₂]) = (0.80)² / (0.10 × 0.10) = 0.64 / 0.010 = 64. Since Δn = 0 (2 moles on each side), Kc has no units in this case. Since Kc >> 1, the equilibrium lies to the right — there is a greater concentration of HI than of H₂ and I₂ at equilibrium

How do you use the magnitude of Kc to estimate the position of equilibrium?

The magnitude of Kc tells you how far the equilibrium lies towards products or reactants:

• Kc >> 1 (e.g. Kc = 10⁶): the equilibrium lies far to the right — products are greatly favoured; the reaction goes nearly to completion.

• Kc ≈ 1: the equilibrium lies roughly in the middle — significant amounts of both reactants and products are present at equilibrium.

• Kc << 1 (e.g. Kc = 10⁻⁶): the equilibrium lies far to the left — reactants are greatly favoured; very little product is formed.

How does changing temperature affect the value of Kc?

Kc is only affected by temperature. For an exothermic forward reaction (ΔH negative), increasing temperature shifts equilibrium to the left, so the concentration of reactants increases and products decreases — the value of Kc decreases. For an endothermic forward reaction (ΔH positive), increasing temperature shifts equilibrium to the right, so Kc increases. Changing concentration, pressure, or adding a catalyst does not change the value of Kc — only the temperature does.